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Three equivalent methods of generating the paperfolding sequence are presented as well as a categorisation of runs of identical terms. We find all repeated subsequences, the largest repeated subsequences and the spacing of singles, doubles and triples throughout the sequence. The paperfolding sequence is shown to have links to the Binary Rejected Gray Code and the Stern-Brocot tree. [ABSTRACT FROM AUTHOR]

This paper proposes some simple propagation rules which give rise to new binary constant-weight codes. [ABSTRACT FROM AUTHOR]

The successive refinement problem is extended to vector sources where individual distortion constraints are posed on each vector component. For vector Gaussian sources with squared-error distortion, a single-letter rate-distortion characterization is inherited from the previously studied Gaussian multiple descriptions problem with covariance distortion constraints. Though this characterization is amenable to well-known numerical convex optimization techniques, an analytical solution is difficult to obtain in full generality even for 2-D sources. In this work, the special case of successive refinability is addressed analytically. Specifically, vector Gaussian sources are shown to be not successively refinable everywhere unlike scalar Gaussian sources. It is also shown that, for 2-D Gaussian sources, the rate loss at the second stage can be as high as 0.5 b/sample in a "degenerate" scenario corresponding to what is known as sequential coding of correlated sources. Finally, analysis of 2-D binary symmetric sources with Hamming distortion reveals that the behavior of these sources with respect to successive refinability exhibits remarkable similarity to their 2-D Gaussian counterparts. [ABSTRACT FROM AUTHOR]

Inaccuracies in computations in the paper of the authors on classification of perfect binary codes of lengths 15 and 16 and of rank 13 are fixed. An explicit construction of all extended perfect codes of length 16 and rank 13 with a given kernel size is presented. Perfect binary codes of length 15 and rank 14 obtained by the general doubling construction are classified. [ABSTRACT FROM AUTHOR]

In this paper, we give three new constructions of binary sequences of period 4N with optimal autocorrelation value or optimal autocorrelation magnitude using N x 4 interleaved sequences. Yu and Gong recently found any binary sequence of period 4N with optimal autocorrelation value constructed from an almost difference set by Arasu et al. is an N x 4 interleaved sequence for which all four columns in its N x 4 array are shift equivalent up to the complement. We found that it is not necessary that four columns are shift equivalent. Instead, it could be a pair of related sequences together with their shifts as the column sequences. The first construction is to use a generalized GMW sequence of period N = 22k - 1 and its modified version, the second construction is to use a twin prime sequence of length N = p(p + 2) and its modified version, and the third construction, a pair of Legendre sequences of period N = p (p odd prime) with their respective first terms complementary (the 2-level autocorrelation property is not needed for the Legendre sequence). The comparison with the known constructions are given. For the new sequences with optimal autocorrelation value, their corresponding new almost difference sets are also derived. [ABSTRACT FROM AUTHOR]

High-performance steganography requires large embedding rate and small distortion, i.e., high embedding efficiency. Steganographic codes (stego-codes) derived from covering codes can improve embedding efficiency. In this paper, a new method is proposed to construct binary stego-codes for LSB embedding in gray-scale signals, which shows that not just one but a family of stego-codes can be generated from a covering code by combining Hamming codes and wet paper codes. This method can greatly expand the set of embedding schemes as applied to steganography. Performances of stego-code families (SCF) of structured codes and random codes are analyzed. SCFs of random codes can approach the rate-distortion bound on LSB embedding for any chosen embedding rate. Furthermore, SCFs are modified for applications in ±1 embedding, and a treble layered embedding method for ±2 embedding is obtained. By combining the modified SCFs and the treble layered method, a near-optimal scheme for ±2 embedding is presented. [ABSTRACT FROM AUTHOR]

In H.264/AVC coders, the optimal mode decision for each coding unit is achieved based on a calculation of the rate distortion (R-D) cost for each candidate mode. In this letter, we propose a context-adaptive binary arithmetic coding (CABAC)- based rate estimation scheme that reduces the computational complexity of the R-D cost function evaluation. The complex and time-consuming calculation of the arithmetic coding is replaced by a table lookup based on the proposed CABAC rate model for fast rate estimation. The context modeling part of CABAC is also simplified to accelerate the rate estimation process. The experimental results show that the proposed estimator follows the actual rate with the coefficient of determination R2 = 0.9997. The proposed estimator yields about a 30% reduction in the computational complexity of the R-D optimized mode decision, thereby accelerating the entire encoder by about 17% to 25% with almost no degradation in the R-D performance. [ABSTRACT FROM AUTHOR]

We investigate a binary code, which is implemented by serially concatenating a multiplexer, a multilevel delay processor, and a signal mapper to a binary turbo encoder. To achieve improved convergence behavior, we modify the binary code by passing only a fraction of the bits in the turbo code through the multilevel delay processor and the signal mapper. Two decoding [ABSTRACT FROM AUTHOR]

Let K = (k1, k2, …, kr) and L = (l1, l2, …, ls) be sets of nonnegative integers. Let F = (F1, F2, …, Fm) be a family of subsets of [n] with [Fi] ϵ K for each i and ∣Fi ∩ Fj∣ ϵ L for any i≠j. Every subset Fe of [n] can be represented by a binary code a = (a1, a2, …, an) such that ai = 1 if i ϵ Fe and ai = 0 if iϵFe. Alon et al. made a conjecture in 1991 in modular version. We prove Alon-Babai-Sukuki's Conjecture in nonmodular version. For any K and L with n ⩾ s + max ki, ∣F∣ ⩽ (n-1 s ) + (n-1 s-1) + … + (n-1 s-2r+1). [ABSTRACT FROM AUTHOR]

Energy consumption of portable RFID readers is becoming an important issue as applications of RFID systems pervade many aspects of our lives. Surprisingly, however, these systems are not energy-aware with the focus till date being on reducing the time to read all tags by the reader. In this work, we consider the problem of tag arbitration in RFID systems with the aim of designing energy-aware anticollision protocols. We explore the effectiveness of using multiple time slots per node of a binary search tree through three ariticollisiori protocols. We further develop an analytical framework to predict the performance of our protocols and enable protocol parameter selection. We demonstrate that all three protocols provide significant energy savings both at the reader and tags (if they are active tags) compared to the existing Query Tree protocol, while sharing the deterministic property of the latter. Further, we show that our protocols provide similar benefits even with correlated tag IDs. [ABSTRACT FROM AUTHOR]

Abstract: A binary image I is B a , W b -connected, where a, b ∈{4,8}, if its foreground is a-connected and its background is b-connected. We consider a local modification of a B a , w b -connected image I in which a black pixel can be interchanged with an adjacent white pixel provided that this preserves the connectivity of both the foreground and the background of I. We have shown that for any (a, b)∈{(4,8), (8,4), (8,8)}, any two B a , w b -connected images I and J each with n black pixels differ by a sequence of Θ(n 2) interchanges. We have also shown that any two B 4, W 4-connected images I and J each with n black pixels differ by a sequence of O(n 4) interchanges. [Copyright &y& Elsevier]

Abstract: We consider hierarchical systems where nodes represent entities and edges represent binary relationships among them. An example is a hierarchical composition of Web services where the nodes denote services and the edges represent the parent–child relationship of a service invoking another service. A fundamental issue to address in such systems is, for two nodes X and Y in the hierarchy, whether X can see Y, that is, whether X has visibility over Y. The visibility could be with respect to certain attributes like operational details, execution logs and security related issues. In a general setting, X seeing Y may depend on (i) X wishing to see Y, (ii) Y wishing to be seen by X, and (iii) other nodes not objecting to X seeing Y. In this paper, we develop a generic conceptual model to express visibility. We study two complementary notions: sphere of visibility of a node X that includes all the nodes in the hierarchy that X can see; and sphere of noticeability of X that includes all the nodes that can see X. We also identify dual properties, coherence and correlation, that relate the spheres of different nodes in special ways and also relate the visibility and noticeability notions. We study some variants of coherence and correlation also. These properties give rise to interesting and useful visibility and noticeability assignments, and their representations. [Copyright &y& Elsevier]

Context-Based Binary Arithmetic Coding (CABAC) is one of two entropy coders used in H.264/AVC, which achieves a high compression ratio at the expense of high computational complexity. For real-time decoding of ultra-high resolution video, we propose a high-throughput hardwired CABAC decoder subsystem. By analyzing the distribution of different types of syntax elements (SE), we propose a Two-Bin arithmetic decoding engine (Two-Bin AE) to generate two bins in one cycle for the most frequent SEs. In order to boost the utilization of the proposed engine, we employ a Prediction-Based Parallel Processing Method to perform decoding and context index calculation in parallel. Furthermore, we propose a Context Table Reallocation Scheme, which can shorten the critical path delay of a Two- Bin AE circuit by 18%. Experimental results show that our decoder on average takes only 118 clock cycles to decode one macroblock (MB) at Main Profile, Level 4.0. For QFHD, i.e., 4×1080 HD, sequences, it can run effectively at 110MHz. The design has been successfully integrated into an H.264/AVC QFHD video decoder in an SOC system. [ABSTRACT FROM AUTHOR]

A method of control is proposed on the basis of representing the checked circuits as consequently connected subcircuits (cascades). The subdivision of the circuits into cascades is made in such a way that any failure in each of them results in a distortion of no more than one binary digit at its input. There is developed an universal sequential-sampling circuit with step-by-step control, where the detection of errors does not require additional (coding) variables. The results of this investigation showed that the proposed method for operational control entails considerably lesser hardware and power expenditure as compared with the circuits based on application of the Berger code. [ABSTRACT FROM AUTHOR]

This work presents a brief survey on codes (with respect to Hamming metric) which are perfect-like i.e. codes which are capable to correct a given set of error vectors and no others. Several kinds of such codes which exist in the literature have been discussed and possibilities of the existence of such codes in some cases have been explored. [ABSTRACT FROM AUTHOR]

Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite alphabet are being compressed into binary sequences by some one-to-one mapping. No a priori information about X is available at the encoder, which must therefore adopt a universal data-compression algorithm. It is known that there exist a number of asymptotically optimal universal data compression algorithms (e.g., the Lempel—Ziv (LZ) algorithm, Context tree algorithm and an adaptive Hufmann algorithm) such that when successively applied to N-blocks then, the best error-free compression for the particular individual sequence X is achieved as N tends to infinity. The best possible compression that may be achieved by any universal data compression algorithm for finite N-blocks is discussed. Essential optimality for the compression of finite-length sequences is defined. It is shown that the LZ77 universal compression of N-blocks is essentially optimal for finite N-blocks. Previously, it has been demonstrated that a universal context tree compression of N blocks is essentially optimal as well. [ABSTRACT FROM AUTHOR]

In this paper, we explain how to build a turbo-like structure with binary inputs and chaotic outputs for efficient coding and decoding in additive white Gaussian noise (AWGN). We analyze the convergence of the decoding algorithm, the performance in the error floor region and explain minimum distance properties of the resulting codes. [ABSTRACT FROM AUTHOR]

In this letter, a tow complexity decoding algorithm for binary linear block codes is applied to low-density parity-check (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity. [ABSTRACT FROM AUTHOR]

In this letter, we propose a tow complexity Maximum Likelihood (ML) decoding algorithm for orthogonal space-time block codes (OSTBCs) based on the real-valued lattice representation and QR decomposition. We show that for a system with rate = K/T, where K is the somber of transmitted symbols per T time slots, the proposed algorithm decomposes the original complex-valued system into a parallel system represented by 2K real-valued components, thus allowing for a simple and independent detection of the real and imaginary parts of each complex transmitted symbol. We further show that for square L-QAM constellations, the proposed algorithm reduces the decoding computational complexity from O(L) for conventional ML to C'(√L) without sacrificing the performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose orthogonal Space-Time (ST) codes for binary Pulse Position Modulations (PPM). Unlike the well known orthogonal ST codes, the proposed schemes verify the additional constraint of achieving a foil transmit diversity order without introducing any phase rotations. This renders the proposed codes suitable for Free-Space Optical (FSO) communications with direct detection and for Ultra-WideBand (UWB) communications. At the receiver side, optimal detection can he achieved with linear operations and the proposed codes can be also applied with On-Off Keying (OOK). [ABSTRACT FROM AUTHOR]

In this paper, we describe and analyze the source and channel coding properties of a class of sparse graphical codes based on compounding a low-density generator matrix (LDGM) code with a low-density parity-check (LDPC) code. Our first pair of theorems establishes that there exist codes from this ensemble, with all degrees remaining bounded independently of block length, that are simultaneously optimal for both channel coding and source coding with binary data when encoding and decoding are performed optimally. More precisely, in the context of lossy compression, we prove that finite-degree constructions can achieve any pair (R, D) on the rate-distortion curve of the binary symmetric source. In the context of channel coding, we prove that the same finite-degree codes can- achieve any pair (C, p) on the capacity-noise curve of the binary symmetric channel (BSC). Next, we show that our compound construction has a nested structure that can be exploited to achieve the Wyner—Ziv bound for source coding with side information (SCSI), as well as the Gelfand—Pinsker bound for channel coding with side information (CCSI). Although the results described here are based on optimal encoding and decoding, the proposed graphical codes have sparse structure and high girth that renders them well suited to message passing and other efficient decoding procedures. [ABSTRACT FROM AUTHOR]

We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to show, interpreting the following notions appropriately, that if a code has a large distance, then its dual has a small covering radius and, therefore, is large. This implies the original code to be small. We also point out that this bound is a natural isoperimetric constant of the Hamming cube, related to its Faber–Krahn minima. While our approach belongs to the general framework of Delsarte’s linear programming method, its main technical ingredient is Fourier duality for the Hamming cube. In particular, we do not deal directly with Delsarte’s linear program or orthogonal polynomial theory. [ABSTRACT FROM AUTHOR]

Given a vector of floating-point numbers with exact sum s, we present an algorithm for calculating a faithful rounding of s, i.e., the result is one of the immediate floating-point neighbors of s. If the sum s is a floating-point number, we prove that this is the result of our algorithm. The algorithm adapts to the condition number of the sum, i.e., it is fast for mildly conditioned sums with slowly increasing computing time proportional to the logarithm of the condition number. All statements are also true in the presence of underflow. The algorithm does not depend on the exponent range. Our algorithm is fast in terms of measured computing time because it allows good instruction-level parallelism, it neither requires special operations such as access to mantissa or exponent, it contains no branch in the inner loop, nor does it require some extra precision: The only operations used are standard floating-point addition, subtraction, and multiplication in one working precision, for example, double precision. Certain constants used in the algorithm are proved to be optimal. [ABSTRACT FROM AUTHOR]

Abstract: Reversible logic has become one of the most promising research areas in the past few decades and has found its applications in several technologies; such as low-power CMOS, nanocomputing and optical computing. This paper presents improved and efficient reversible logic implementations for Binary Coded Decimal (BCD) adder as well as Carry Skip BCD adder. It has been shown that the modified designs outperform the existing ones in terms of number of gates, number of garbage outputs, delay, and quantum cost. In order to show the efficiency of the proposed designs, lower bounds of the reversible BCD adders in terms of gates and garbage outputs are proposed as well. [Copyright &y& Elsevier]

It is shown that subclasses of separable binary Goppa codes, Γ(L, G) - codes, with L = {α ϵ GF(221) : G(α) ≠ 0} and special Goppa polynomials G(x) can be presented as a chain of embedded and equivalent codes. The true minimal distance has been obtained for all codes of the chain. [ABSTRACT FROM AUTHOR]

Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that many codes in the family meet the Griesmer bound and therefore are length-optimal. New distance-optimal binary QC [195, 8, 96], [210, 8, 104], and [240, 8, 120] codes, and good ternary QC [208, 6, 135] and [221, 6, 144]codes are also obtained by the construction. [ABSTRACT FROM AUTHOR]

Abstract  We investigate further the new approach towards the classification of periodic binary sequences into nonlinear complexity classes that commenced in the paper by Petrides and Mykkeltveit (Proceedings of SETA’06 international conference on sequences and their applications, 2006). Nonlinear complexity was first introduced by Jansen (Investigations on nonlinear streamcipher systems: construction and evaluation methods, PhD thesis, 1989) and several attempts have since been made to make it of more practical cryptographic interest. In this direction, we will follow with this article. In particular we perform composition of the recursions found in the (2006) article which are related to nonlinear complexity, and prove some of its missing results. Studying the properties of the composition operation for a certain type of recursions is an alternative to study all possible recursions, as required for completing the above mentioned classification. A complete classification will allow, amongst other things, construction of statistical tests to assess the cryptographic strength of binary sequences used in stream ciphers. [ABSTRACT FROM AUTHOR]

Abstract  By counting the coset leaders for cosets of weight 3 of the Melas code we give a new proof for the characterization of Kloosterman sums divisible by 3 for $${\mathbb{F}_{2^m}}$$ where m is odd. New results due to Charpin, Helleseth and Zinoviev then provide a connection to a characterization of all $${a\in\mathbb{F}_{2^m}}$$ such that $${Tr(a^{1/3})=0}$$; we prove a generalization to the case $${Tr(a^{1/(2^k-1)})=0}$$. We present an application to constructing caps in PG(n, 2) with many free pairs of points. [ABSTRACT FROM AUTHOR]

This correspondence investigates iterative soft-in-soft-out (SISO) detection in coded multiple access channels, with Gray-coded M-ary quadrature amplitude modulation (QAM) for the channel symbols. The proposed solution may be summarized as a generic iterative detection scheme called bit-level equalization and soft detection (BLESD), which is an extension of a unified variational inference framework for binary SISO detection proposed in our prior work. This new strategy fundamentally differs from the conventional symbol detector, in that data symbols are transparent to the new detector. Rather, soft estimates of the bits that make up the symbols are directly and naturally obtained by the detector in terms of posterior probabilities given the channel observation, facilitating efficient message-passing in joint detection and decoding. Case studies that illustrate the applications of the proposed scheme are presented for turbo multiuser detection (MUD) for multiple-access interference (MAI) channels and turbo equalization for inter-symbol interference (ISI) channels. [ABSTRACT FROM AUTHOR]

The performance of punctured low-definition parity-check (LDPC) codes under maximum-likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their average weight distributions (AWDs) and the corresponding asymptotic growth rate of the AWDs. In particular, it is proved that capacity-achieving codes of any rate and for any memoryless binary-input output-symmetric (MBIOS) channel under ML decoding can be constructed by puncturing some original LDPC code with small enough rate. Moreover, it is shown that the gap to capacity of all the punctured codes can be the same as the original code with a small enough rate. Conditions under which puncturing results in no rate loss with asymptotically high probability are also given in the process. These results show high potential for puncturing to be used in designing capacity-achieving codes, and in rate-compatible coding under any MBIOS channel. [ABSTRACT FROM AUTHOR]

Abstract: Colloidal crystals formed by two types of polystyrene particles of different sizes (94 and 141 nm) at various number ratios (94:141 nm) are studied. Experiments showed that the formation time of crystals lengthens as the number ratio of the two components approaches 1:1. The dependence of the mean interparticle distance , crystal structure and alloy structure on the number ratio of the two types of particles was studied by means of Kossel diffraction technique and reflection spectra. The results showed that as the number ratio decreased, the mean interparticle distance became larger. And the colloidal crystal in binary mixtures is more preferably to form the bcc structure. This study found that binary systems form the substitutional solid solution (sss)-type alloy structure in all cases except when the number ratio of two types of particles is 5:1, which results instead in the superlattice structure. [Copyright &y& Elsevier]

The authors discuss predictions made by software and technology companies and suggest that in many cases software engineers predicted far greater future advances and innovations than they actually produced. Software engineers use source codes to write instructions for executable codes. However, these codes are limited, and many developers began using more complex binary and proprietary codes.

BIT BY BIT is an encryption game that is designed to improve students' understanding of natural language processing in computers. Participants encode clear words into binary code using an encryption key and exchange them in the game. BIT BY BIT enables participants who do not understand the concept of binary numbers to perform the process of converting decimal into binary and vice versa. This understanding helps participants to comprehend one of the concepts of computer science (i.e., how computers express natural languages using signals). [ABSTRACT FROM AUTHOR]

The classification of binary [n, k, d] codes with d ⩾ s2k -1 and without zero coordinates is reduced to the classification of binary [(2k - 1)c(k,s,t) + t,k,d] code for n =(k - 1)s + t, s ⩾ 1 and 1 ⩽ t ⩽ - 2k - 2, where c(k, s, t) ⩽ min{s, t} is a function of k, s, and t. Binary [15s + t, 4] optimal self-orthogonal codes are characterized by systems of linear equations. Based on these two results, the complete classification of [15s + t,4] optimal self-orthogonal codes fort t Є {1,2,6,7,8,9,13,14} and s ⩾ 1 is obtained, and the generator matrices and weight polynomials of these 4-dimensional optimal self-orthogonal codes are also given. [ABSTRACT FROM AUTHOR]

We examine the performance of genetic algorithms using binary encoding, with respect to a change of basis. Changing the basis can result in a change in the linkage structure inherent in the fitness function. We test three simple functions with differing linkage strengths and analyze the results. Based on an empirical analysis, we show that a better basis results in a smoother fitness landscape, hence genetic algorithms based on the new encoding method provide better performance. [ABSTRACT FROM AUTHOR]

Abstract: Babu and Chowdhury [H.M.H. Babu, A.R. Chowdhury, Design of a compact reversible binary coded decimal adder circuit, Journal of Systems Architecture 52 (5) (2006) 272–282] recently proposed, in this journal, a reversible adder for binary-coded decimals. This paper corrects and optimizes their design. The optimized 1-decimal BCD full-adder, a 13×13 reversible logic circuit, is faster, and has lower circuit cost and less garbage bits. It can be used to build a fast reversible m-decimal BCD full-adder that has a delay of only m +17 low-power reversible CMOS gates. For a 32-decimal (128-bit) BCD addition, the circuit delay of 49 gates is significantly lower than is the number of bits used for the BCD representation. A complete set of reversible half- and full-adders for n-bit binary numbers and m-decimal BCD numbers is presented. The results show that special-purpose design pays off in reversible logic design by drastically reducing the number of garbage bits. Specialized designs benefit from support by reversible logic synthesis. All circuit components required for optimizing the original design could also be synthesized successfully by an implementation of an existing synthesis algorithm. [Copyright &y& Elsevier]

We introduce a fully parametric approach for updating beliefs regarding correlated binary variables, after marginal probability assessments based on information of varying quality are provided by an expert. This approach allows for the calculation of a predictive joint density for future assessments. The proposed methodology offers new insight into the parameters that control the dependence of the binary variables, and the relation of these parameters to the joint density of the probability assessments. A comprehensible elicitation procedure for the model parameters is put forward. The approach taken is motivated and illustrated through a practical application. [ABSTRACT FROM AUTHOR]

A framework that generates formal prefix equations for speculative carry generation is presented. It is applicable to both normal carry and Ling carry adders and generates four forms of speculative carry generate prefix schemes (two forms for each carry case). For normal carry, one corresponds to an existing design and the other is newly introduced. For the Ling carry, both are newly proposed. [ABSTRACT FROM AUTHOR]

Fingerprinting provides a means of tracing unauthorized redistribution of digital data by individually marking each authorized copy with a personalized serial number. In order to prevent a group of users from collectively escaping identification, collusion-secure fingerprinting codes have been proposed. In this paper, we introduce a new construction of a collusion-secure fingerprinting code which is similar to a recent construction by Tardos but achieves shorter code lengths and allows for codes over arbitrary alphabets. We present results for ‘symmetric’ coalition strategies. For binary alphabets and a false accusation probability $$\varepsilon_1$$ , a code length of $$m\approx \pi^2 c_0^2\ln\frac{1}{\varepsilon_1}$$ symbols is provably sufficient, for large c 0, to withstand collusion attacks of up to c 0 colluders. This improves Tardos’ construction by a factor of 10. Furthermore, invoking the Central Limit Theorem in the case of sufficiently large c 0, we show that even a code length of $$m\approx 1/2\pi^2 c_0^2\ln\frac{1}{\varepsilon_1}$$ is adequate. Assuming the restricted digit model, the code length can be further reduced by moving from a binary alphabet to a q-ary alphabet. Numerical results show that a reduction of 35% is achievable for q = 3 and 80% for q = 10. [ABSTRACT FROM AUTHOR]

The covering radius of binary 2-surjective codes of maximum length is studied in the paper. It is shown that any binary 2-surjective code of M codewords and of length $$n = {M-1 \choose \left\lfloor(M-2)/2\right\rfloor}$$ has covering radius $$\frac{n}{2} - 1$$ if M - 1 is a power of 2, otherwise $$\left\lfloor\frac{n}{2}\right\rfloor$$ . Two different combinatorial proofs of this assertion were found by the author. The first proof, which is written in the paper, is based on an existence theorem for k-uniform hypergraphs where the degrees of its vertices are limited by a given upper bound. The second proof, which is omitted for the sake of conciseness, is based on Baranyai’s theorem on l-factorization of a complete k-uniform hypergraph. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of low-rate error correction codes called repeat-zigzag-Hadamard (RZH) codes featuring simple encoder and decoder structures, and flexible coding rate. RZH codes are serially concatenated turbo-like codes where the outer code is a repetition code and the inner code is a punctured zigzag-Hadamard (ZH) code. By analyzing the code structure of RZH codes, we prove that both systematic and nonsystematic RZH codes are good codes, in the sense that for an RZH code ensemble, there exists a positive number γo such that for any binary-input memory less channel whose Bhattacharyya noise parameter is less than γo, the average block error probability of maximum-likelihood (ML) decoding approaches zero. Two decoding algorithms-serial and parallel decoders for RZH codes-are proposed. We then employ the extrinsic information transfer (EXIT) chart technique to design irregular RZH codes. Results show that the optimized irregular RZH codes exhibit a performance that is very close to capacity in the low-rate regime. [ABSTRACT FROM AUTHOR]

We show that the linear complexity of a u2 v -periodic binary sequence, u odd, can easily be calculated from the linear complexities of certain 2 v -periodic binary sequences. Since the linear complexity of a 2 v -periodic binary sequence can efficiently be calculated with the Games-Chan algorithm, this leads to attractive procedures for the determination of the linear complexity of a u2 v -periodic binary sequence. Realizations are presented for u  = 3, 5, 7, 15. [ABSTRACT FROM AUTHOR]

Local binary patterns (LBPs) are one of the features which have been used for texture classification. In this paper, a method based on using these features is proposed for fabric defect detection. In the training stage, at first step, LBP operator is applied to an image of defect free fabric, pixel by pixel, and the reference feature vector is computed. Then this image is divided into windows and LBP operator is applied to each of these windows. Based on comparison with the reference feature vector, a suitable threshold for defect free windows is found. In the detection stage, a test image is divided into windows and using the threshold, defective windows can be detected. The proposed method is multiresolution and gray scale invariant and can be used for defect detection in patterned and unpatterned fabrics. Because of its simplicity, online implementation is possible as well. [ABSTRACT FROM AUTHOR]

Conventionally, in each low-density parity-check (LDPC) decoding iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (flooding schedule). An alternative, more efficient, approach is to update the nodes' messages serially (serial schedule). A theoretical analysis of serial message passing decoding schedules is presented. In particular, the evolution of the computation tree under serial scheduling is analyzed. It shows that the tree grows twice as fast in comparison to the flooding schedule's one, indicating that the serial schedule propagates information twice as fast in the code's underlying graph. Furthermore, an asymptotic analysis of the serial schedule's convergence rate is done using the density evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that for long codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule, when working near the ensemble's threshold. This observation is generally proved for the binary erasure channel (BEC) under some natural assumptions. Finally, an accompanying concentration theorem is proved. [ABSTRACT FROM AUTHOR]

Starting from a succession rule for Catalan numbers, we define a procedure for encoding and listing the objects enumerated by these numbers such that two consecutive codes of the list differ only by one digit. The Gray code we obtain can be generalized to all the succession rules with the stability property: each label ( k) has in its productions two labels c 1 and c 2, always in the same position, regardless of k. Because of this link, we define Gray structures as the sets of those combinatorial objects whose construction can be encoded by a succession rule with the stability property. This property is a characteristic that can be found among various succession rules, such as the finite, factorial or transcendental ones. We also indicate an algorithm which is a very slight modification of Walsh’s one, working in O(1) worst-case time per word for generating Gray codes. [ABSTRACT FROM AUTHOR]

A chip-interleaved randomly spread direct-sequence code-division multiple-access (DS-CDMA) scheme is considered, employed in two variants of Wyner's infinite linear cell-array model with fiat fading. Focusing on the asymptotic setup in which both the number of users per cell and the processing gain go to infinity, while their ratio (the ‘cell load’) goes to some finite constant, the spectral efficiencies of the optimum and linear minimum mean-squared error (MMSE) joint multicell receivers are investigated. A dramatic performance enhancement as compared to single-cell-site processing is demonstrated. The asymptotic behavior of the two receivers in extreme signal-to-noise ratio (SNR) regimes and in a high cell-load regime are analyzed as well. The impact of chip interleaving versus symbol interleaving is also investigated. Chip-level interleaving is found beneficial in several cases of interests, and is conjectured to be beneficial in general. [ABSTRACT FROM AUTHOR]

In this correspondence, a relay rate-constrained variation of the three-node relay channel is introduced and studied. In the rate-constrained relay channel, the relay cannot reliably decode or encode beyond a rate constraint -R. A cut-set upper bound, and rate-constrained variation of decode-and-forward and estimate-and-forward protocol are derive 1. It is observed that relative performance of the unconstrained protocols does not predict relative performance of the constrained protocols; that is, estimate-and-forward almost always offers superior performance for a mall rate constraints. A new metric, denoted as the relay efficiency, measures the slope at which the relay channel rate increases over the relay-less channel. While the cut-set upper bound has a relay efficiency of one for the Gaussian relay channel at - = 0, the two new protocols do not. Finally, it is shown that an effective relay rate constraint can be computed for general relay protocols. To demonstrate this concept, a Markovian amplify-and-forward protocol, in which the relay does not perform any explicit encoding or decoding, is examined and compared to the introduced rate constrained protocols. [ABSTRACT FROM AUTHOR]

With the growing popularity of decimal computer arithmetic in scientific, commercial, financial and Internet-based applications, hardware realisation of decimal arithmetic algorithms is gaining more importance. Hardware decimal arithmetic units now serve as an integral part of some recently commercialised general purpose processors, where complex decimal arithmetic operations, such as multiplication, have been realised by rather slow iterative hardware algorithms. However, with the rapid advances in very large scale integration (VLSI) technology, semi- and fully parallel hardware decimal multiplication units are expected to evolve soon. The dominant representation for decimal digits is the binary-coded decimal (BCD) encoding. The BCD-digit multiplier can serve as the key building block of a decimal multiplier, irrespective of the degree of parallelism. A BCD-digit multiplier produces a two-BCD digit product from two input BCD digits. We provide a novel design for the latter, showing some advantages in BCD multiplier implementations. [ABSTRACT FROM AUTHOR]

The effect of plasma microfields on Coulomb collisions between the particles is considered. It is shown that perturbations from other particles insignificantly affect the frequency of short-range collisions. The results of calculating the pair correlation function of the particles in a plasma for distances much shorter than the interparticle distance agree well with predictions of the binary theory. [ABSTRACT FROM AUTHOR]

Abstract  A pointed variety of universal algebras is protomodular in the sense of D. Bourn, if and only if it is classically ideal determined in the sense of A. Ursini (this result is due to D. Bourn and G. Janelidze). We prove a characterization theorem for pointed protomodular categories, which is a (pointed) categorical version of Ursini’s characterization theorem for classically ideal determined varieties, involving classically 0-regular algebras. A suitable simplification of the property of a pair of relations, which is used to define a classically 0-regular algebra, yields a new closedness property of a single binary relation – we show that a finitely complete pointed category is protomodular if and only if every binary internal relation R→A 2 in it has this closedness property. [ABSTRACT FROM AUTHOR]